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A156052 Triangle read by rows: t(n,m)=Binomial[n, m]/Beta[n + 1, n - m + 1] + Binomial[n, n - m]/Beta[n + 1, m + 1]. 0
2, 8, 8, 33, 48, 33, 144, 240, 240, 144, 635, 1240, 1260, 1240, 635, 2778, 6510, 6720, 6720, 6510, 2778, 12019, 33600, 38430, 33600, 38430, 33600, 12019, 51488, 168672, 223776, 184800, 184800, 223776, 168672, 51488, 218799, 824400, 1275120, 1119888 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{2, 16, 114, 768, 5010, 32016, 201698, 1257472, 7777314, 47800080, 292292946,...}.

LINKS

Table of n, a(n) for n=0..39.

FORMULA

t(n,m)=Binomial[n, m]/Beta[n + 1, n - m + 1] + Binomial[n, n - m]/Beta[n + 1, m + 1].

EXAMPLE

{2},

{8, 8},

{33, 48, 33},

{144, 240, 240, 144},

{635, 1240, 1260, 1240, 635},

{2778, 6510, 6720, 6720, 6510, 2778},

{12019, 33600, 38430, 33600, 38430, 33600, 12019},

{51488, 168672, 223776, 184800, 184800, 223776, 168672, 51488},

{218799, 824400, 1275120, 1119888, 900900, 1119888, 1275120, 824400, 218799},

{923790, 3939210, 7025040, 6966960, 5045040, 5045040, 6966960, 7025040, 3939210, 923790},

{3879887, 18476920, 37451700, 42488160, 31741710, 24216192, 31741710, 42488160, 37451700, 18476920, 3879887}

MATHEMATICA

Clear[f];

f[n_, m_] = Binomial[ n, m]/Beta[n + 1, n - m + 1] + Binomial[n, n - m]/Beta[n + 1, m + 1];

Table[Table[f[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A064231 A181130 A212196 * A170923 A083523 A202619

Adjacent sequences:  A156049 A156050 A156051 * A156053 A156054 A156055

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 02 2009

STATUS

approved

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Last modified November 16 23:51 EST 2018. Contains 317275 sequences. (Running on oeis4.)